Gravity from a fermionic condensate of a gauge theory

Abstract

The most prominent realization of gravity as a gauge theory similar to the gauge theories of the standard model comes from enlarging the gauge group from the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan gravity the symmetry must be broken, which can be accomplished by known quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle physics and condensed matter systems, we propose that the symmetry can naturally be broken by a homogenous and isotropic fermionic condensate of ordinary spinors. We demonstrate that the condensate is compatible with the Einstein-Cartan equations and can be imposed in a fully de Sitter invariant manner. This lends support, and provides a physically realistic mechanism for understanding gravity as a gauge theory with a spontaneously broken local de Sitter symmetry.